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22 November, 12:43

The light intensity of a source in 100 candelas. The illuminance on a surface is 4 lux. How far is the surface from the source?

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  1. 22 November, 12:48
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    The answer is 5 meters.

    The illuminance on a surface (E) is equal to the light intensity (I) divided by the square distance from the light source (d):

    E = I : d² [=] candela / square meters = lux.

    The unit of the illuminance is lux.

    So, it is given:

    E = 4 lux

    I = 100 candelas

    d = ?

    If:E = I : d²

    Then

    d² = I : E

    ⇒ d² = 100 : 4

    ⇒ d² = 25

    If we put both sides of the equation under the square root, then:

    √d² = √25

    ⇒ d = 5 meters.

    Therefore, the surface is 5 meters far from the light source.
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